"Calculate the gravitational potential energy at the surface of the sun. How much would the sun have to shrink each second in order to generate the Luminosity of the sun just by converting gravitational potential energy?" The hint my teacher gave us was to use dU/dt and set it equal to the luminosity of the sun ( dU/dt = L). I know that gravitational potential energy is U = GMm/r, and our teacher told us to use 1 kg for m if needed, so the first part of this problem wasn't bad. However, my solution to the second part was wrong, and I'd like to know how it should've been solved. If anyone could show me, I'd appreciate it.